The mean of a single flipped coin is 0
The mean of two flips is 0.5
The mean of ten flips is 0.3
The mean of twentyfive flips is 0.44
The mean of twenty five thousand flips is 0.5023333
Hypothesis Testing
POLS 3316: Statistics for Political Scientists
2023-10-15
Fresh Check Day (Mental Health Awareness) in Lynn Eusan Park https://uh.edu/wellness/calendar/?view=e&id=640121#event
Midterm corrections due one week from today
You are free to use any resource except:
- the answer sheet from the last time I taught the class
- another person
- cheating sites such as Chegg, Course Hero, etc.
- I would recommend the lecture slides as your main resource
A falsifiable statement about what we believe will happen based on the theory we are trying to test.
alternative hypothesis or H1
alternative hypothesis or H1
alternative hypothesis or H1
null hypothesis or H0
NO!!!!
If we reject the null we infer that the alternative hypothesis is approximately true within the probability we have chosen.
How do we get from a sample with a correlation to talking about testing a hypothesis for a population?
How do we get from a sample with a correlation to talking about testing a hypothesis for a population?
68-95-99.7 Rule
68-95-99.7 Rule
+ Allows us to estimate probability based on distance from the mean
68-95-99.7 Rule
+ Allows us to estimate probability based on distance from the mean
+ Applies to normal distribution
The 68-95-99.7 Rule
+ Allows us to estimate probability based on distance from the mean
+ Applies to normal distribution
+ Basis for the actual decision rules
68-95-99.7 rule
+ Population - The entire group we want to draw conclusions about
+ Population - The entire group we want to draw conclusions about
+ Sample - The subset of the population that we draw data from
+ Population - The entire group we want to draw conclusions about
+ Sample - The subset of the population that we draw data from
+ The sample is a random subset of the population
+ Population - The entire group we want to draw conclusions about
+ Sample - The subset of the population that we draw data from
+ The sample is a random subset of the population
+ A good sample is representative of the population
+ Population - The entire group we want to draw conclusions about
+ Sample - The subset of the population that we draw data from
+ The sample is a random subset of the population
+ A good sample is representative of the population
Two tools tie sample statistics to estimates of the true population parameters: standard error and z-score
Two tools tie sample statistics to estimates of the true population parameters: standard error and z-score
+ The standard error is a special case of the standard deviation
Two tools tie sample statistics to estimates of the true population parameters: standard error and z-score
+ The standard error is a special case of the standard deviation
+ The z-score is a fairly simple math problem involving subtracting two numbers and dividing by the standard error
Two tools tie sample statistics to estimates of the true population parameters: standard error and z-score
+ The standard error is a special case of the standard deviation
+ The z-score is a fairly simple problem involving subtracting two numbers and dividing by the standard error
+ Bonus: the z-score is one of our hypotheses test values for large sample sizes
Two tools tie sample statistics to estimates of the true population parameters: standard error and z-score
+ The standard error is a special case of the standard deviation
+ The z-score is a fairly simple problem involving subtracting two numbers and dividing by the standard error
+ Bonus: the z-score is one of our hypotheses test values for large sample sizes
+ Extra bonus: the cutoff point for the z-score in a hypothesis test is really easy to remember
Two rules to tie the sample to probability distributions and population estimates:
+ **The Central Limit Theorem**
+ **The Law of Large Numbers**
The mean of a single flipped coin is 0
The mean of two flips is 0.5
The mean of ten flips is 0.3
The mean of twentyfive flips is 0.44
The mean of twenty five thousand flips is 0.5023333
The CLT begins to apply at a sample size around 30
The sample size we need is determined by a number of things including the degree of certainty we are looking for
Want to do some polling? This is where margin of error comes from:
margin of error
Stephen Moore code used to simulate the Law of Large Numbers
Author: Tom Hanna
Website: tomhanna.me
License: This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.</>
GOVT2306, Fall 2023, Instructor: Tom Hanna